Perfluoroalkyleneethertriazine oligomer obtained by reacting a dinitrile compound NC--Rf.sup.0 --CN, where Ff.sup.0 is --(CFXOCF.sub.2)a(CF.sub.2)b(CF.sub.2 OCFX)c--, where X is a fluorine atom or a CF.sub.3 group, a is an integer of 1 to 5, b is an integer of 1 to 2 and c is an integer of 1 to 5, or Rf.sup.0 is --CF.sub.2 O(CF.sub.2 O)dCF.sub.2 --, where d is an integer of 1 to 8, with ammonia, further reacting the resulting diamizine compound with a dinitrile compound NC--RF.sup.1 --CN, RF.sup.1 has the same meaning as that for Rf.sup.0 or Rf.sup.1 is a perfluoroalkylene group having 4 to 8 carbon atoms thereby obtaining a perfluoroalkyleneetherpolyimidoyamizine oligomer, then reacting the resulting oligomer with a perfluoronitrile compound Rf.sup.2 CN, Rf.sup.2 is CF.sub.3 (OCF.sub.2).sub.e -- where e is an integer of 3 to 10 thereby treating the terminal groups thereof, and then subjecting the resulting terminal-treated oligomer to a ring-closing reaction with a perfluoroacylating agent RF.sup.3 COY, Rf.sup.3 is CF.sub.3 (OCF.sub.2).sub.f -- where f is an integer of 3 to 10 has a good resistance to oxidation in the presence of a metal at a high temperature, and can improve the heat resistance of a perfluoropolyetherpolytetrafluoroethylene powder-based grease, when added therto.